Question

[Hàn Mộ Dii]

1) Phân tích hằng đẳng thức:

a/ (12x - 5)²

b/ (4x² - y)³

c/ (7x + 8)³

2) Phân tích đa thức thành nhân tử:

a/ x³ - 16x

b/ x² - 12x + 36

c/ 1 - 8x³

d/ 1/25x² - 1/64y²

e/ (x + 2xy)³ - (x - 2y)³

f/ -x³ + 9x² - 27x + 27

3) Tìm x, biết:

a/ x² - 8x + 16 = 0

b/ x² - x + 1/4 = 0

c/ 5x(x - 1000) - x + 1000 = 0

*hạn: trước 11/10/2017

Answer 1

[Ngọc Hiền]

\(1,a,\left(12x-5\right)^2=12^2x^2-2.12.5x+5^2\)

\(b,\left(4x^2-y\right)^3=\left(4x^2\right)^3-3.\left(4x^2\right)^2y+3.4x^2.y^2-y^3=4x^6-3.16x^4y+12x^2y^2\)

\(c,\left(7x+8\right)^3=\left(7x\right)^3+3.\left(7x\right)^28+3.7x.8+8^3\)

Answer 2

[Ngọc Hiền]

\(a,x^3-16x=x\left(x^2-16\right)=x\left(x^2-4^2\right)=x\left(x-4\right)\left(x+4\right)\)

\(b,x^2-12x+36=x^2-2.x.6+6^2=\left(x-6\right)^2\)

\(1-8x^3=1^3-\left(2x\right)^3=\left(1-2x\right)\left(1^2+1.2x+\left(2x\right)^2\right)=\left(1-2x\right)\left(1+2x+4x^2\right)\)

\(d,\dfrac{1}{25}x^2-\dfrac{1}{64}y^2=\left(\dfrac{1}{5}x\right)^2-\left(\dfrac{1}{8}x\right)^2=\left(\dfrac{1}{5}x-\dfrac{1}{8}x\right)\left(\dfrac{1}{5}x+\dfrac{1}{8}x\right)=x\left(\dfrac{1}{5}-\dfrac{1}{8}\right)\left(\dfrac{1}{5}+\dfrac{1}{8}\right)\)